English
adjoint
Pronunciation
  • IPA: /ˈædʒ.ɔɪnt/
Adjective

adjoint (not comparable)

  1. (mathematics) Used in certain contexts, in each case involving a pair of transformations, one of which is, or is analogous to, conjugation (either inner automorphism or complex conjugation).
  2. (mathematics, category theory, of a functor) That is related to another functor by an adjunction.
  3. (geometry, of one curve to another curve) Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.
    • 1933, H. F. Baker, Principles of Geometry, 2010, Volume 5, page 103 ↗,
      The sets A + A0, B + B0, together, form the complete intersection, with f = 0, of a composite adjoint curve of order m + k, consisting of the adjoint curve of order m through A + B, together with the non-adjoint curve ω = 0; and the set B + B0 consists of p points, and lies on i + j adjoint φ-curves of f = 0.
    • 1963, Julian Lowell Coolidge, A History of Geometrical Methods, page 205 ↗,
      As we have stated before, a curve f' is adjoint to a curve f if it have at least the multiplicity r_i-1 at each point where f has the multiplicity r_i. A first polar \sum_i y_i \left ( \partial f / \partial x_i \right ) = 0 is an example of an adjoint curve.
    • 2016, Eugene Wachspress, Rational Bases and Generalized Barycentrics: Applications to Finite Elements and Graphics, page 216 ↗,
      This imposes n(n - 3)/2 conditions on the n-gon adjoint curve.
Synonyms
  • (mathematics) adjunct (in certain contexts)
Related terms Translations Noun

adjoint (plural adjoints)

  1. (mathematics) The transpose of the cofactor matrix of a given square matrix.
  2. (mathematics, linear algebra, of a matrix) Transpose conjugate.
  3. (mathematics, analysis, of an operator) Hermitian conjugate.
  4. (mathematics, category theory) A functor related to another functor by an adjunction.
  5. (geometry, algebraic geometry) A curve A such that any point of a given curve C of multiplicity r has multiplicity at least r–1 on A. Sometimes the multiple points of C are required to be ordinary, and if this condition is not satisfied the term sub-adjoint is used.
  6. An assistant to someone who holds a position in the military or civil service.
  7. An assistant mayor of a French commune.
Translations
  • German: Adjungierte
  • Spanish: matriz de adjuntos, matriz de cofactores


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